laser and fourier transform emission spectroscopy of the...

JOURNAL OF MOLECULAR SPECTROSCOPY 184, 186–201 (1997)ARTICLE NO. MS977301

Laser and Fourier Transform Emission Spectroscopyof the G4F–X 4F System of TiF

R. S. Ram,* J. R. D. Peers,† Ying Teng,† A. G. Adam,† A. Muntianu,‡ P. F. Bernath,* ,‡ and S. P. Davis§

*Department of Chemistry, University of Arizona, Tucson, Arizona 85719; †Department of Chemistry, University of New Brunswick, Frederiction,New Brunswick, Canada E3B 6E2; ‡Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; and

§Department of Physics, University of California, Berkeley, California 94720

Received November 25, 1997; in revised form March 11, 1997

The emission spectrum of the G 4F–X 4F transition of TiF has been observed in the region 13 500–16 000 cm01 usinga Fourier transform spectrometer (FTS), as well as by laser excitation spectroscopy. In the FTS experiments the bandswere excited in a carbon tube furnace by the reaction of titanium metal vapor with CF4 at a temperature of about 23007C.In the laser experiments the TiF molecules were produced by laser vaporization of a Ti rod followed by reaction withSF6 using a pulsed supersonic jet source. Three groups of bands with high-wavenumber subband heads at 14 388,15 033, and 15 576 cm01 have been assigned as 0–1, 0–0, and 1–0 vibrational bands of the G 4F–X 4F transition,respectively. Each vibrational band consists of four subbands assigned as 4F3/2– 4F3/2 , 4F5/2– 4F5/2 , 4F7/2– 4F7/2 , and4F9/2– 4F9/2 . A rotational analysis has been performed and molecular constants for the ground and excited states havebeen extracted using the combined FTS and laser excitation measurements. The correspondence between the electronicstates of TiF, TiH, and Ti/ has also been discussed. q 1997 Academic Press

INTRODUCTION spectra of M-type stars (13) . The recent observation of AlFin the atmosphere of a carbon star (14, 15) and the presenceof HF in numerous red giant stars (16) also strengthen theTransition metal-containing molecules are of current inter-

est because of their importance in astrophysics (1–3) and possibility that transition metal fluorides such as TiF, VF,and CrF may also be found. A positive identification ofcatalysis (4, 5) . Many theoretical calculations have been

carried out, often with the goal of understanding the nature transition metal fluorides could provide a direct estimate ofthe fluorine abundance in stars.of metal–ligand interactions (6–8) . These molecules are

also of importance in high-temperature chemistry. To date only limited spectroscopic information is avail-able on the halides of titanium. There are several low-resolu-In general the electronic spectra of diatomic molecules

containing transition elements are very complex. Many tran- tion studies of the TiF (17, 18) , TiCl (19–21) , TiBr (22,23) , and TiI (24) molecules. The spectra of these moleculessition metal elements have open d-shells which results in a

high density of electronic states, and these states often have have been investigated in the visible region and a 4P– X 4S0

transition has been tentatively identified between 380 andhigh multiplicity and large orbital angular momenta. Thespectra are further complicated by spin–orbit interactions 440 nm. In particular there are two independent analyses of

TiF bands in the region 380–440 nm. In one study Diebnerand perturbations between the close-lying electronic states.The analysis of the spectra of transition metal-containing and Kay (17) observed the absorption spectra of TiF be-

tween 390 and 410 nm and proposed a ground state vibra-molecules, however, provides valuable information aboutchemical bond formation and molecular structure. Surpris- tional frequency of 593 cm01 , while in another study Cha-

talic et al. (18) obtained the same bands in emission andingly, the spectroscopic properties of many transition metalhalides are poorly known experimentally, particularly in proposed a different vibrational assignment with a ground

state vibrational frequency of 607.1 cm01 . Neither of thesecomparison with the corresponding oxides and hydrides.The spectra of diatomic molecules containing 3d transi- two values for the vibrational frequency turn out to be cor-

rect. In these low-resolution studies the bands were classifiedtion elements are prominent in the spectra of cool stars andsunspots (2, 3, 9–13) . Titanium-containing molecules are into four subbands, namely 4P01/2– 4S0 , 4P1/2– 4S0 ,

4P3/2– 4S0 , and 4P5/2– 4S0 .particularly important because Ti has a high cosmic abun-dance. The presence of TiO and TiH has been well estab- The assignment of a 4S0 ground state for TiF (17, 18)

was based on a primitive theoretical calculation by Carlsonlished in the atmospheres of cool stars. For example, TiOhas been identified in the spectra of M-type stars (2, 3, 9) and Moser (25) for the isoelectronic VO molecule. How-

ever, the 4P– 4S0 assignment for this transition has beenand sunspots (10–12) while TiH has been observed in the

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THE G 4F–X 4F SYSTEM OF TiF 187

questioned by Shenyavskaya and Dubov (26) for TiF and obtained, providing the first high-resolution spectroscopicdata for all four spin components of the ground state of TiF.by Phillips and Davis (27) for TiCl. Rotational analysis of

some of the TiF bands previously assigned to the 4P– 4S0 Many bands with complex structure remain to be analyzedin the region 4000–14 000 cm01 . The observation of thetransition (17, 18) was obtained by Shenyavskaya and Du-

bov (26) , who reassigned them as 2F– 2D and 2D– 2D tran- G 4F–X 4F transition in laser excitation experiments using amolecular beam source also confirms that the lower state ofsitions. In another study Phillips and Davis (27) rotationally

analyzed a few visible bands of TiCl and also assigned them this transition is most probably the ground state of TiF.to a 2F– 2D transition.

In our previous studies of transition metal fluorides (28, EXPERIMENTAL DETAILS29) and hydrides (30, 31) we have noticed that there is aone-to-one correspondence between the low-lying electronic The TiF bands have been observed in two different experi-states of transition metal hydrides and fluorides. The corre- ments: Fourier transform emission spectroscopy at the Na-spondence between hydrides and fluorides is well known in tional Solar Observatory in Tucson, Arizona, and laser va-spectroscopy although it has not been much exploited. A porization spectroscopy at the University of New Brunswick,comparison of the available data for TiF (17, 18, 26) with Canada. The details for each experiment will be providedthose for TiH (32–35) suggests that the assignment of a separately.4S0 or a 2D ground state for TiF is unlikely since TiH isknown to have a 4F ground state. 1. Fourier Transform Emission Spectroscopy

There are only a limited number of theoretical studies oftitanium monohalide molecules (36) . A crude prediction of The emission spectra of TiF were produced by the reaction

of titanium metal vapor with CF4 in a high-temperature car-the low-lying electronic states of TiF was obtained by Cambi(36) using the semiempirical computational method devised bon tube furnace at a temperature of about 23007C. The

initial experiment was intended to record improved spectraby Fenske et al. (37) . This calculation predicted a 4S0

ground state followed by 2D, 4F, and 4P states at higher of the 1-mm system of TiH which has been previously re-corded by two of the authors using a hollow cathode sourceenergy. Recently, an ab initio study of TiF has been carried

out by Harrison (38) , who has calculated the spectroscopic (42) . In this experiment about 90 Torr H2 was added alongwith about 100 Torr He as a buffer gas. The TiH bands wereproperties of a number of doublet and quartet states. This

work predicts a 4F ground state for TiF consistent with the observed very weakly, and we decided to search for theanalogous transition of TiF using the same experimentalTiH results. According to Harrison’s calculations there is a

low-lying 4S0 state which is about 0.1 eV above the X 4F conditions but using CF4 instead of H2. When a small amountof CF4 was added, numerous strong bands were observedstate. This calculation also predicts that the lowest-lying

doublet state is the 2F state which lies about 0.65 eV above from 4000 to 16 000 cm01 . The bands in the region 4000–13 000 cm01 are very complex in appearance because ofthe ground 4F state.

A mass spectroscopic study of TiF along with TiF2 and overlapping from neighboring bands. Some of these bandsprobably do not belong to TiF since the intervals betweenTiF3 has been carried out by Zmbov and Margrave (39) .

This work establishes the relative stability of TiF2 and TiF3 the rotational lines are too large for TiF. The weaker bandsobserved in the region 13 500–16 000 cm01 , however, arethrough equilibrium measurements and provides an estimate

of 136 { 8 kcal/mole for the dissociation energy of TiF. relatively free from overlapping and were readily identifiedas belonging to a single transition with the 0–0 band nearThe strong Ti–F bond improves the chances of forming TiF

in stellar atmospheres, particularly in AGB stars. A Ti–F 15 033 cm01 . This transition has been named the G 4F–X 4Ftransition by comparing the TiF and TiH energy level dia-bond length of 1.754 A has been obtained for TiF4 from an

electron diffraction experiment by Petrov et al. (40) . Several grams as will be discussed below.The emission from the furnace was focused onto the 8-unsuccessful attempts were made to record the ESR spec-

trum of TiF in rare gas matrices by DeVore et al. (41) and mm entrance aperture of the 1-m Fourier transform spec-trometer of the National Solar Observatory at Kitt Peak. Thethey concluded that the ground state of TiF was most proba-

bly not a 4S0 as assigned previously (17, 18) . spectra were recorded using silicon photodiode detectors andRG 645 filters at a resolution of 0.02 cm01 . A total of sixIn the present paper we report on the observation of a

4F– 4F transition of TiF in the region 14 000–16 000 cm01 . scans were coadded in about 30 min of integration and thespectra had a signal-to-noise ratio of about 15:1.This transition has been assigned as the G 4F–X 4F transition

based on the recent theoretical predictions of Harrison (38) The spectral line positions were determined using a datareduction program called PC-DECOMP developed by J.and on the experimental and theoretical information avail-

able for the TiH molecule (32–35) . The rotational analysis Brault. The peak positions were determined by fitting a Voigtlineshape function to each line. The present spectra wereof the 0–1, 0–0, and 1–0 bands of this transition has been

Copyright q 1997 by Academic Press

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RAM ET AL.188

calibrated using the laser measurements (described in thefollowing section) of a number of lines of the 0–0 and 1–0 bands of TiF. The molecular lines appear with a typicalwidth of 0.07 cm01 and the line positions are expected tobe accurate to about {0.005 cm01 . However, since there isconsiderable overlapping and blending caused by the pres-ence of different subbands in the same region, the error inthe measurement of blended and weak lines is expected tobe somewhat higher.

2. Laser Excitation SpectroscopyFIG. 1. A compressed portion of the low-resolution spectrum of the

G 4F–X 4F transition of TiF.The apparatus used to create the TiF molecule in the mo-lecular beam work has been described previously (43, 44) ;however, some details pertinent to this work will be given.

region three groups of bands have been observed with theA titanium target in the form of a slowly rotating andhigh-wavenumber R heads at 14 383, 15 033, and 15 576translating rod was ablated by about 6 mJ of 355-nm radia-cm01 (Fig. 1) , assigned as the 0–1, 0–0, and 1–0 vibrationaltion from a Nd:YAG laser. At the same time, a gas mixturebands, respectively. The next members in the D£ Å 01, 0,of 0.8% SF6 seeded in helium was passed from a pulsed1 sequences (the 1–2, 1–1, and 2–1 bands) could not bemolecular beam valve into the ablation region. Vaporizedidentified because of their weaker intensity and overlappingtitanium was entrained by the gas mixture and then expandedfrom the stronger main bands. The 0–2 and 2–0 bands couldthrough a short expansion channel into a vacuum chamber,not be identified in our spectra because of their very weakproducing a molecular jet.intensity. In the 0–1 and 1–2 band region there is a weakTiF molecules are formed through reaction of the hot Tihead-like structure near 14 150 cm01 but this band probablyatoms with SF6 and its decomposition products during thebelongs to another transition. To lower wavenumbers thereexpansion process. About 5 cm downstream from the nozzleare additional weak heads near 13 230, 13 600, and 14 690orifice, the molecules were probed with a tunable dye laser.cm01 , which may be associated with the 14 150 cm01 band.For low-resolution studies the laser was a Lumonics pulsedAll of these bands are degraded toward lower wavenumbersdye laser, while for high-resolution spectra the laser was a(red degraded) and have weak R heads.Coherent 699-29 ‘‘Autoscan’’ cw ring dye laser. Laser-in-

The structure of each of these bands is very complexduced fluorescence was collected orthogonally to both thebecause of overlapping from different subbands. A Hund’smolecular beam and the probe laser and imaged on a 0.25-case (a) 4F– 4F transition consists of four main subbandsm monochromator. Light passing through the monochroma-4F3/2– 4F3/2 , 4F5/2– 4F5/2 , 4F7/2– 4F7/2 , and 4F9/2– 4F9/2 ,tor was detected by a cooled photomultiplier tube. The signalwhich are separated by three times the difference betweenwas amplified, integrated, and sent either to a chart recorderthe spin–orbit coupling constants of the upper and loweror to the computer controlling the Autoscan laser system.electronic states. The V-assignment in different subbands isDCM dye was used in both lasers to record spectra for theconfirmed by the Beff values in the different spin components0–0 and 1–0 bands of the G 4F–X 4F transition. Typicalwith B(4F9/2 ) ú B(4F7/2 ) ú B(4F5/2 ) ú B(4F3/2 ) as ex-linewidths were about 0.1 cm01 for the low-resolution scans,pected for a regular 4F state (see Discussion). In contrastlimited by the laser linewidth, and about 180 MHz for theto the laser experiments, no first lines were seen in the FTShigh-resolution scans where the limitation was residualexperiments.Doppler broadening in the molecular beam. The line posi-

A schematic energy level diagram of the 4F– 4F transitiontions were measured using the Autoscan system, which hasis presented in Fig. 2. The subband order in each vibrationala specified absolute frequency accuracy of {200 MHz andband is 4F9/2– 4F9/2 , 4F7/2– 4F7/2 , 4F5/2– 4F5/2 , and 4F3/2–a precision of {60 MHz. Calibration of the Autoscan system4F3/2 in order of increasing wavenumbers. It was noticedwas maintained by recording a section of the I2 spectrumthat the 0–0 and 0–1 bands of the 4F5/2– 4F5/2 and 4F3/2–and comparing the line positions with the values published4F3/2 subbands lie very close to each other, separated byin the I2 atlas (45) .only 0.18 cm01 . This is a coincidence since all four heads

DESCRIPTION OF OBSERVED BANDS were found to be well separated in the 1–0 band. Parts ofthe 0–0 and 1–0 bands are presented in Fig. 3 where the

1. Fourier Transform Emission Spectroscopy heads due to the four subbands in each band have beenmarked. These observations also suggest that the groundThe TiF bands assigned to the G 4F–X 4F transition are

located in the spectral region 13 000 to 16 000 cm01 . In this state is a well-behaved 4F state in which all of the four spin


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perturbed region were not definitely identified because ofstrong overlapping and irregular spacing. In fact in the 0–1 band no rotational lines could be identified for J * valuesabove 56.5. The £ Å 1 vibrational level of the G 4F3/2 spincomponent is also perturbed. In this vibrational level pertur-bations are found in two regions: the first perturbation isobserved at J * Å 21.5 and the other perturbation is observedat J * Å 31.5. At this early stage of analysis the sourceof these perturbations is unclear, although there are manypossibilities (e.g., F 4D state) .

The subbands with 0–0 heads located at 15 032.8,15 024.0, and 15 009.5 cm01 have been assigned to the5/2–5/2, 7/2–7/2, and 9/2–9/2 subbands, respectively.No rotational perturbations have been observed in any ofthese subbands. The 7/2–7/2 and 9/2–9/2 subbands areweaker in intensity and are strongly overlapped by 3/2–3/2 and 5/2–5/2 subbands. The rotational lines of thesesubbands were not obvious at first glance and again the useof our Loomis–Wood program was essential in identifyingthe rotational lines. An expanded portion of the 0–0 bandnear the R heads of the 4F3/2– 4F3/2 , 4F5/2– 4F5/2 , and4F7/2– 4F7/2 subbands is presented in Fig. 4.

2. Laser Excitation SpectroscopyFIG. 2. A schematic energy level diagram of the G 4F–X 4F transition

Two vibrational bands of the G 4F–X 4F system of TiFof TiF with arrows marking the observed subbands. The band origins fordifferent subbands are also listed. were recorded in the molecular beam experiments, the 0–0

and 1–0 bands. An attempt was made to record the 0–1band but this band showed up only weakly in the pulseddye laser scans and lies in a region where the DCM dyecomponents have similar vibrational intervals whereas inlaser falls off rapidly in laser power. No high-resolution datathe excited state the four spin components have differentcould be obtained for the 0–1 band.vibrational intervals. This results in a different subband pat-

A comparison between the FTS data and the moleculartern for the 1–0 band as compared to that in the 0–0 and0–1 bands. The excited G 4F state is interacting with a close-lying state (or states) not observed in this work.

At first glance the spectra appear very complex and thelines belonging to the high-wavenumber subbands were theonly ones to be clearly identified. However, a careful inspec-tion of the spectra using a Loomis–Wood program providedthe lines of all four spin components. The structure of eachof the four subbands consists of R and P branches consistentwith the DV Å 0 assignment. No Q branches were detectedin any of the subbands (in FTS spectra) and no transitionswhich violate the Hund’s case (a) selection rule DS Å 0could be identified. This means that we are unable to directlydetermine any intervals between the spin components fromthe FTS measurements alone. V-doubling is not observed inany of the subbands as expected for a 4F– 4F transition.

The R head at 15 033 cm01 has been identified as the 0–0 band of the 3/2–3/2 subband. No V-doubling was ob-served even for the highest J values observed. The £ Å 0vibrational level of the G 4F3/2 spin component is perturbed FIG. 3. A portion of the 0–0 and 1–0 bands of the G 4F–X 4F system

of TiF. The R-head positions of different subbands have been marked.between J* Å 56.5 and 65.5 and several of the lines in the


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RAM ET AL.190

subband R head at 15 032.8 cm01 and the dye laser wasscanned to higher wavenumber. In this way, a transitionfrom the X 4F3/2 spin component to the G 4F5/2 spin compo-nent could be observed by monitoring the strong fluores-cence back to the X 4F5/2 spin component. We were able toobserve a signal when the laser was scanned 101.84 cm01

(with an error of perhaps 10 cm01) higher in wavenumber.

ANALYSIS AND RESULTS

The rotational assignments in the different bands weremade by comparing combination differences for the commonvibrational levels. Since no transitions involving DS x 0were observed in the FTS spectra, the subbands of differentspin components were initially fitted separately using a sim-

FIG. 4. An expanded portion of the 0–0 band of the G 4F–X 4F system ple empirical term energy expression (Eq. [1]) , even thoughof TiF near the R heads of the 4F3/2– 4F3/2 , 4F5/2– 4F5/2 , and 4F7/2– 4F7/2 the lower 4F state obeys Hund’s case (a) coupling. The termsubbands.

energy expression for a spin component with no V-doublingis

beam data is given in Figs. 4 and 5. The FTS data for the F£(J) Å T

£/ B

£J(J / 1) 0 D

£[J(J / 1)]2

[1]0–0 band, Fig. 4, clearly show the problem of overlapping/ H

£[J(J / 1)]3 / L

£[J(J / 1)]4 .lines from the different subbands. This was not a problem

in the molecular beam work, Fig. 5. Even in the closelyspaced R-head region of the overlapping 3/2–3/2 and The lines from both FTS and laser measurements were ulti-5/2–5/2 subbands, we were able to resolve the lines. All mately combined and fitted simultaneously. The initial band-of the branches could be followed easily from the first lines by-band fit of different subbands provided similar constantsout to about J Å 20.5 where the signal becomes too weak. for common vibrational levels, confirming the vibrationalIn all, data were recorded for the 3/2–3/2, the 5/2–5/2, assignments. In the final fit, the lines of all of the vibrationaland the 7/2–7/2 subbands in both the 0–0 and 1–0 vibra- bands in each subband were combined and fitted simultane-tional bands of the G 4F–X 4F system. R , P , and Q branches ously. The observed line positions for the different subbandswere observed for these subbands. of G 4F–X 4F are provided in Table 1. For the transitions

The transitions for the 9/2–9/2 subband were too weakin intensity to be recorded with the ring laser, presumablybecause the X 4F9/2 spin component lies three spin–orbitintervals above the X 4F3/2 spin component and therefore hasonly a small population in the molecular beam. The samepopulation argument also leads us to believe that the lower4F electronic state involved in this transition must be theground state. Given that the transitions from the X 4F9/2 spincomponent and from the £ 9 Å 1 level for the ground state(the vibrational spacing is about 650 cm01) are weak, evenin the pulsed dye laser experiments, it is reasonable to as-sume that a low-lying electronic state such as the 4S0 statewhich is calculated to be 0.1 eV (800 cm01) higher than theX 4F state will not be populated in the molecular beam.

As in the FTS spectra, no lines violating the Hund’s case(a) selection rule, DS Å 0, could be recorded. However, itwas possible to measure the spin–orbit interval between theX 4F3/2 and X 4F5/2 levels. This was accomplished in a pulsedlaser experiment. Narrow slits were used in a small mono-chromator with a resolution of about {2 nm. The monochro- FIG. 5. A portion of the laser excitation spectrum of the 0–0 band near

the R heads of the 4F3/2– 4F3/2 and 4F5/2– 4F5/2 subbands.mator was then set to observe fluorescence of the 5/2–5/2


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TABLE 1Observed Line Positions ( in cm01 ) for the G 4F–X 4F Transition of TiF


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RAM ET AL.192

TABLE 1—Continued


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TABLE 1—Continued


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RAM ET AL.194

TABLE 1—Continued


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TABLE 1—Continued


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RAM ET AL.196

TABLE 1—Continued

for which both laser and FTS measurements are available, attempt was made to fit all of the observed lines using the4 1 4 matrix appropriate for Hund’s case (a) 4F state (Tableonly the laser measurements are provided in this table. The

rotational lines were weighted according to resolution, extent 4) . A free fit of all the subbands was unsuccessful becauseof the effects of global perturbations. Note the large numberof blending, and effects of perturbations. Badly blended lines

were heavily deweighted. The effective molecular constants of effective rotational constants needed in the excited statein the empirical analysis (Table 3). The ground state casefor the lower and excited 4F states are provided in Tables

2 and 3, respectively. (a) rotational constants, however, were determined from afit of the combination differences. In this fit the spin–orbitAt a later stage in the analysis, a spin–orbit interval of 101.84

cm01 was measured between the X 3F3/2 and X 3F5/2 spin com- parameter A was fixed to 33.95 cm01 , a value determinedfrom the observed spacing of 101.84 cm01 (3A) betweenponents from the laser excitation experiments. Therefore, an


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TABLE 2Effective Molecular Constants ( in cm01 ) for the X 4F State of TiF

the 3/2 and 5/2 spin components. The case (a) molecular and H0 ligands give rise to similar energy level patterns inconstants for £ Å 0 of the X 4F state are provided in Table TiF and TiH, although the bonding in TiH is expected to be5. In this fit only lines with J £ 30.5 were used and the much more covalent than that in TiF.RMS error of the fit was 0.008 cm01 . When the range of J The lowest energy term of the Ti/ atom is a 4F whichwas extended, the quality of the fit deteriorated. arises from the 3d 24s 1 configuration (46) . This 4F term

correlates to the X 4F, A 4S0 , B 4P, and C 4D states in TiHand TiF (Fig. 6) . The first excited term in Ti/ is b 4F atDISCUSSIONÇ1000 cm01 , arising from the 3d 3 configuration (46) . TheTiF and TiH molecular states correlating to b 4F are 4S0 ,Prior to the present work very limited spectroscopic infor-4D, 4F, and 4P (Fig. 6) . From Fig. 6 it appears that themation was available for TiF. The initial theoretical studygeneral picture of the low-lying states of TiH and TiF canof TiF by Cambi (36) is not very reliable. A reliable predic-be predicted from the Ti/ energy levels, although the order-tion of the spectroscopic properties of TiF requires the useing of states corresponding to a particular atomic term isof high-level ab initio calculations with large basis sets anddifficult to predict and may change on going from hydrideextensive electron correlation. A recent calculation by Har-to fluoride. The third Ti/ term, a 2F (3d 24s 1) , at 4700 cm01 ,rison (38) is a giant step forward, at least for the low-lyingcorrelates with the a 2D, b 2P, c 2F, and d 2S0 states of TiH.states.

The detailed energy ordering as presented in Fig. 6 isIn our previous studies of transition metal fluorides andprobably not completely correct. However, we are suffi-hydrides we have noted a close similarity between the elec-ciently confident of the qualitative correctness of Fig. 6 thattronic transitions. A detailed comparison for the CoH/CoF,we use the letter labels G 4F–X 4F for our new transition.FeH/FeF, and ScH/ScF pairs has been reported previouslyThe ground X 4F electronic state of TiF is derived from(28–30) . It has been concluded that the low-lying electronicthe metal-centered s 1p 1d 1 configuration. According to thestates of transition metal hydrides, MH, and fluorides, MF,theoretical predictions of Harrison (38) , the lowest excitedalso correlate directly with the states of the M/ atom. Therequartet state is the A 4S0 state, located at 0.1 eV. This stateis a very high-quality set of ab initio calculations for TiHarises from the s 1d 2 configuration. The next higher excited(35) which can be compared with the available results forstates, B 4P and C 4D, arise from s 1p 1d 1 and p 2d 1 configura-TiF (38) . The correlation diagram of the electronic statestions, respectively. There are two low-lying metal-centeredof TiF, TiH, and Ti/ provided in Fig. 6 suggests that their

energy levels share a remarkably similar pattern. The F0 s orbitals (nominally 4ss and 3ds) and the G 4F–X 4F tran-


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RAM ET AL.198

TABLE 3Effective Molecular Constants ( in cm01 ) for the G 4F State of TiF

sition results from shifting an electron from the lower energy values obtained in this work. We note that the visible spectraare extremely complicated and several of the observed bandss orbital to the higher s orbital.

The ground state of TiH is known to be X 4F on the basis (which could be the missing spin components) were leftunassigned.of both experimental observations (32–34) and theoretical

calculations (35) . However, there has been controversy over The DG(1/2) values of the four spin components X 4F3/2

(650.61 cm01) , X 4F5/2 (650.68 cm01) , X 4F7/2 (650.74the nature of the ground electronic state of TiF (17, 18, 38) .The early low-resolution work on TiF by Diebner and Kay cm01) , and X 4F9/2 (650.78 cm01) are nearly identical, con-

sistent with a well-behaved case (a) 4F state. A similar(17) and Chatalic et al. (18) suggested a 4S0 ground state,supported by the prediction of Cambi (36) . In contrast to comparison of the excited state vibrational intervals for

G 4F3/2 (542.69 cm01) , G 4F5/2 (531.71 cm01) , G 4F7/2this, another study of the TiF molecule at grating resolutionby Shenyavskaya et al. (19) favors a 2D ground state. The (526.82 cm01) , and G 4F9/2 (526.62 cm01) shows the effects

of strong interactions with other states.most recent theoretical prediction on TiF by Harrison (38) ,however, predicts a 4F ground state. This assignment is also Since the constants for the four spin components of the

4F states have been determined by treating each spin compo-consistent with the results available for TiH, from both ex-perimental (32–34) and theoretical studies (35) . nent as an individual state, the determination of ‘‘true’’

Hund’s case (a) constants from the effective constants isA comparison of the rotational constants of Shenyavskayanecessary. A simple perturbation theory analysis of the 4 1et al. (19) with the values obtained in the present work4 matrix representation of the energy levels of a 4F stateindicates that their £ Å 0 2D3/2 rotational constants agreeleads to the following relationships:very well with our constants for £ Å 0 of the 4F3/2 spin

component. This indicates that their 2D3/2 state is most prob-Beff (3/2) Å B(1 0 B /A) [2a]ably the X 4F3/2 spin component. However, there seems to

be some problems in their analysis of the bands involvingBeff (5/2) Å B(1 0 B /3A) [2b]

£ 9 Å 1 since their constants for £ 9 Å 1 and their value ofDG 9(1/2) Å 675 cm01 do not agree with the corresponding Beff (7/2) Å B(1 / B /3A) [2c]


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TABLE 4Matrix Elements for a Hund’s Case (a ) X 4F statea,b

Beff (9/2) Å B(1 / B /A) . [2d]

TABLE 5 In these equations A is the usual spin–orbit coupling con-Case (a ) Molecular Constants for the X 4F stant and B is the ‘‘true’’ rotational constant associated with

Ground State of TiF the 4F state. A quick check using Eqs. [2a] – [2d] leads tothe conclusion that both the G 4F and X 4F states are regular(A ú 0). Equations [2a] – [2d] work surprisingly well con-sidering that the subband origins are spaced so irregularly.For example, for £ Å 0 in the X 4F state Beff (5/2) 0 Beff

(3/2) Å 0.002233 cm01 , Beff (7/2) 0 Beff (5/2) Å 0.002394cm01 , and Beff (9/2) 0 Beff (7/2) Å 0.002449 cm01 whichgives B90 Å 0.3682 cm01 and A90 Å 38 cm01 by simpleaveraging. For the excited G 4F state B *0 Å 0.3356 cm01 andA*0 Å 37 cm01 . The spin–orbit intervals (3A) are thus about114 cm01 in the X 4F state and about 111 cm01 in the G 4Fstate. The observed 3/2–5/2 ground state spin–orbit inter-a Fixed at the value determined by the spin–orbitval of 101.84 cm01 and the Hund’s case (a) B 9 value ofspacing of the 3/2 and 5/2 spin components, 3A Å0.368173 (27) cm01 (Table 5) are in excellent agreement101.84 cm01 , ignoring the small contribution of g,

as determined in the laser excitation experiments. with the corresponding values extracted from the empiricalb Fixed at the value as determined from a fit only constants.

to the molecular beam data. Including the FTS data The equilibrium internuclear separation re was found bygave a strong degree of correlation between g and

using effective B0 and B1 values for each spin componentAD.to calculate effective Be values and then averaging them toc The numbers in parentheses are one standard de-

viation in the last digits. obtain a ‘‘true’’ Be value. Using this algorithm for the X 4F


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RAM ET AL.200

A. The G 4F–X 4F transition is analogous to the 1-mm transi-tion of TiH (42) . The similarity between the electronic en-ergy levels of TiF, TiH, and Ti/ has been discussed. Morework, both experimental and theoretical, is necessary tostraighten out the spectroscopy of the titanium, zirconiumand hafnium monohalides. We have already started on thistask by recording new infrared and near-infrared spectra ofTiCl and ZrCl.

ACKNOWLEDGMENTS

We thank J. Wagner and C. Plymate of the National Solar Observatoryfor assistance in obtaining the spectra. The National Solar Observatory isoperated by the Association of Universities for Research in Astronomy,Inc., under contract with the National Science Foundation. The researchdescribed here was supported by funding from the NASA laboratory astro-physics program. Support was also provided by the Petroleum ResearchFund administered by the American Chemical Society and the NaturalSciences and Engineering Research Council of Canada. We thank J. Har-rison for providing the results of his calculations prior to publication.

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laser and fourier transform emission spectroscopy of the...

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